Find all antiderivatives for the following function Check your work by taking the derivalive, \( f(x)=10 \sec ^{2} x \) The antiderivalives of \( f(x)=10 \sec ^{2} x \) are \( F(x)=\square \)

June 2018 ZIMSEC Paper 1 Solve the equations: \( e^{2 x}=4 e^{2-x} \) giving the answer in exact form. November 2010 ZIMSEC Paper 1

اجد التكامل غير المحدود للدالة \( f(x) = 3x^2 \).

(b) Solve the following first order differential equations. i) \( \frac{d y}{d x}=4 x^{3}-8 x+7 \) kena tambah 1 ii) \( x \frac{d y}{d x}=5 x^{3}+4 \) iii) \( y^{3} \frac{d y}{d x}=\frac{e^{4 x}+4 x}{y} \)

\( \lim _ { x \rightarrow 0 } \frac { 3 ( x - \operatorname { cts } x ) } { x } \)

Calcule \( \int \frac{x^{4} - 5x^{2} + 6}{x-2} \,dx \) aplicando o método de divisão longa.